Recent content by ccox

I don't know but it would be a finite number Any help would be appreciated

A point a in the reals is called a cluster of E if (E intersection(a-r,a+r) contains infinitely many points for every r>0.

Prove that a is a cluster point of E if and only if the set (E intersection (a-r,a+r))\{a} is nonempty for each r > 0. I have the forward implication done but the backwards implication is giving me some trouble. Could you explain it to me.

Here is the problem Let f be differentiable on (0,infinity) if the limit as x approaches infinity f'(x) f(x) both exist are finite prove that limit as x approaches infitity f'(x)=0. I have trouble proving this problem I was told to use Mean Value Theorem to find a contridiction. However...